Cross-Sections of Leech Lattice

Theorem

Except for dimensions $10$, $11$ and $13$, the densest possible sphere packing in all dimensions lower than $24$ can be obtained by cross-sections of the $24$-dimensional space Leech lattice arrangement.


Proof


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Sources

  • Jan. 1984: N.J.A. Sloane: The Packing of Spheres (Scientific American Vol. 250, no. 1: pp. 116 – 125)
  • 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $24$
  • 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $24$
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